Orthogonal polynomials on the unit circle, $q$-Gamma weights, and discrete Painlev\'e equations
Classical Analysis and ODEs
2010-07-06 v2
Abstract
We consider orthogonal polynomials on the unit circle with respect to a weight which is a quotient of -gamma functions. We show that the Verblunsky coefficients of these polynomials satisfy discrete Painlev\'e equations, in a Lax form, which correspond to an surface in Sakai's classification.
Cite
@article{arxiv.0901.0947,
title = {Orthogonal polynomials on the unit circle, $q$-Gamma weights, and discrete Painlev\'e equations},
author = {Philippe Biane},
journal= {arXiv preprint arXiv:0901.0947},
year = {2010}
}
Comments
26 pages 2 figures